LESSON 1 BASIC TRIGONOMETRIC FUNCTIONS SINE COSINE AND

LESSON 1: BASIC TRIGONOMETRIC FUNCTIONS SINE, COSINE, AND TANGENT

I) WHAT IS TRIGONOMETRY? Study of the relationship between the angles in a right triangle with the lengths of the sides Basic trigonometry deals mainly with Right Triangles There are three basic trigonometry functions Sine, Cosine, and Tangent [look for them on your calculator] These trig. Functions will give you the ratios of the sides in a right triangle What do these numbers represent?

II) NAMING SIDES OF A RIGHT TRIANGLE When naming the sides of a R. T. , they are relative to the angle that you are using H Hypotenuse Opposite Side H Adjacent Side Hypotenuse A O A Adjacent Side Opposite Side O Note: The Adjacent and Opposite side can be switched around depending on which angle you use. Note: The Hypotenuse must be the longest side and opposite from the “box” When using Trig, make sure you calculator is on “DEG” mode Deg – Degree Mode

III) SOH-CAH-TOA The Trig. Function that you use depends on which sides of a Right Triangle are given SOH-CAH-TOA If you have or want to find either the “opposite” or “Hypotenuse” sides, then use “SINE” If you have or want to find either the “adjacent” or “Hypotenuse” sides, then use “COSINE” If you have or want to find either the “opposite” or “adjacent” sides, then use “Tangent”

Ex: Indicate which sides are given: Opp, Adj, or Hyp Then indicate which trig function should be used to solve the triangle a) b) c) d) e) f)

III) FINDING MISSING SIDES The first step is to identify which sides are given, make sure you name the sides based on the angle Using the sides that are given, determine which trig. function to use: SOH - CAH - TOA Write the equation and then use algebra to find the missing side Make sure your calculator is in DEG mode!! O A

Ex: Find the length of the missing sides: a) d) b) e) c) f)

EX: FIND THE MISSING SIDES TO 2 DECIMAL PLACES USING TANGENT Cross Multiply!

EX: FIND THE MISSING SIDES TO 2 DECIMAL PLACES Cross Multiply!

EX: FIND THE MISSING SIDES TO 2 DECIMAL PLACES Cross Multiply!

IV) USING TRIG TO FIND MISSING ANGLES If you are finding the angles, use the inverse trig functions First determine which sides are given and which trig function can be used O A Make sure you keep at least 3 to 4 decimal places for your angles NOTE: You can only “Inverse Tan” a ratio, it gives you the angle

Ex: Find the degree of the missing angle:

PRACTICE: FIND THE DEG OF THE MISSING ANGLE

PRACTICE: FIND THE MISSING ANGLE TO THE NEAREST DEGREE

Q: Given each of the following values below, which of the following can sinθ not be equal to?

KEY IDEAS: Pythagorean Thm. Cheong’s Line O A

CHALLENGE: TWO BUILDING ARE 70 METERS APART. THE SHORTER BUILDING IS 50 M HIGH. A CABLE IS ATTACHED TO BOTH BUILDING. THE ANGLE OF INCLINATION IS 15°. HOW TALL IS THE TALLER BUILDING?

SIZE OF A TRIANGLE DON’T MATTER The tangent ratio is used when you are given the “Opposite” and “Adjacent” sides of a R. T. Your calculator must be in “Deg” mode (Degree) The angle doesn’t change whe you have a larger similar triang because the RATIO stays the sa Measure the angle: When you “Tan” the angle, it be equal to the RATIO of the opposite side divided by the adjacent side

III) COSINE RATIO The Cosine ratio is used when you are given the “Adjacent” side and “Hypotenuse” of a R. T. Measure the angle: When you “Cos” the angle, it be equal to the RATIO of the Adjacent side divided by the Hypotenuse